Individual values (Japanese: 個体値individual values), abbreviated IVs, and sometimes referred to as determinant values (DVs) in the context of Generations I and II, are the Pokémon equivalent of genes. They are instrumental in determining the stats of a Pokémon, being responsible for the large variation in stats among untrained Pokémon of the same species.

Generation I and II

In Generation I and II, only four IVs are stored for each individual Pokémon: Attack, Defense, Speed, and Special. Each of these is used to determine their associated stat, with the HP IV determined from the IVs stored for the other four. IVs range from 0-15 (in binary 0000-1111).

The HP IV is calculated by taking the least significant bit (the final binary digit) of the Attack, Defense, Speed, and Special IVs, then creating a binary string by placing them in that order. As such, a Pokémon with an odd-number Attack IV has 8 added to its HP IV, an odd-number Defense IV has 4 added, an odd-number Speed IV has 2 added, and an odd-number Special IV has 1 added.

In Generation II, due to the Special stat being split into Special Attack and Special Defense, the Special IV is used for both Special Attack and Special Defense.

Gender

In Generation II, a Pokémon's gender is determined based solely on its Attack IV when compared to a value specific to each Pokémon species. A Pokémon is female if its Attack IV is less than or equal to its species' gender code, otherwise it is male. For species that are exclusively one gender or have no gender, the calculation based on the Attack IV is ignored.

Due to this calculation, it is impossible to obtain a female Pokémon with high Attack, unless the Pokémon is a member of an all-female species like Jynx or Chansey. Starter Pokémon and others with a gender ratio of seven males to one female suffer the most, with the maximum Attack IV for a female Pokémon of those species being 1.

Shininess

In Generation II, whether or not a Pokémon is Shiny is determined by its IVs.

A Pokémon is Shiny if and only if both of the following conditions are met.

Its Defense, Speed, and Special IVs are all 10.

Its Attack IV is 2, 3, 6, 7, 10, 11, 14, or 15.

Except when IVs are influenced due to breeding, this set of IVs has a 1/8192 chance of occurring, which is also the likelihood of a wild Pokémon being Shiny in Generation III, IV, and V. Due to HP IV being calculated from the other IVs, a Shiny Pokémon's HP IV can only be 0 (if the Attack IV is even) or 8 (if the Attack IV is odd).

Example
For two Sandshrew caught in Union Cave (Sandshrew A is Shiny, Sandshrew B is not Shiny):

Pokémon

Gender

HP

Attack

Defense

Speed

Sp. Atk

Sp. Def

Sandshrew A

♀

22

14

16

11

8

9

8(1000)

7(0111)

10(1010)

10(1010)

10(1010)

Sandshrew B

♀

22

14

17

10

8

9

7(0111)

6(0110)

15(1111)

7(0111)

5(0101)

Unown's letter

In Generation II, Unown's letter is taken from the combination of the center two bits of the Attack, Defense, Speed and Special IV nibbles. This combination is then divided by ten, and the result is rounded down (floor[]) to only include the integer part of the number. This integer will range from 0-25, corresponding to a letter in the Latin alphabet, which will be the Unown's letter (where 0=A, 1=B, 2=C, ..., 23=X, 24=Y, 25=Z).

In Generation II, due to this method of calculating Unown's letter and the way that Shiny Pokémon are determined, a Shiny Unown can only exist in the shape of the letter I or V. Additionally, due to this method of calculating Unown's letter, only 6 combinations correspond to Unown Z, whereas 10 combinations correspond to every other Unown, making Unown Z less common.

In Generation III, Unown's letter is determined by the Pokémon's personality value. From Generation IV onward, it is determined by a separate form identifier. Generation III also introduced Unown '!' or '?'.

Hidden Power

The calculated Type and Power of the move Hidden Power is based on the IVs of the Pokémon. Hidden Power can be of any type aside from Normal, and can have a power between 31 and 70. The formula used in Generation II is different to the one used in later generations.

The move's type is determined by the two least significant bits of the Attack and Defense IVs. The move's power is determined by the most significant bit of each of the Pokémon's IVs, as well as the two least significant bits of the Special IVs.

Generation III onward

In Generation III, the IV system was completely overhauled; now, IVs range from 0-31 rather than 0-15, with HP and Special Defense getting their own independent IVs.

Since IVs now have twice the range, they now have half the influence on a Pokémon's stats. The EV system overhaul and the addition of Natures also result in small changes to formula used to determine stats. The personality value was introduced in Generation III, which handles a Pokémon's gender and Shiny status instead, as well as several other properties; in Generation III, Unown's form was also handled using the personality value, but this is stored separately in Generation IV onward.

The overhaul of the Pokémon data structure is one of the reasons why it was not made possible to trade between Generation II and Generation III games.

Usage

Determination of stats

From Generation III onward, a Pokémon's stats are determined according to the following formulas.

Hidden Power

The calculated Type and Power of the move Hidden Power is based on the IVs of the Pokémon. Hidden Power can be of any type aside from Normal, and prior to Generation VI, have a power between 30 and 70.

The least significant bit of each IV determines the move's Type, and the second-least significant bit of each determines the move's Power.

Characteristic

From Generation IV onward, each Pokémon has a characteristic, a small blurb that indicates which of the Pokémon's IVs is the highest in a roundabout way. Rather than explicitly stating it, one of 30 of these short sentences is chosen, depending on which of the six stats the highest IV is in and how much more than a multiple of five it is.

Breeding

Starting in Generation VI, if either of a Pokémon's parents were holding a Destiny Knot, the child will inherit 5 of its 6 IVs from its parents.

Storage

IVs are now all stored together as a single 32-bit value. Since IVs require 30 bits to be stored, the two most significant bits of this value are used to store other data.

In Generation III, the most significant bit specifies which of two Abilities a Pokémon has (if it has potential to have more than one). If the Pokémon's species can have only one Ability in Generation III, the Ability bit is forced to 0 by the game (if it is forced to be 1, "No ability" will be listed as the Pokémon's Ability).

In Generation IV onward, the most significant bit instead specifies whether or not the Pokémon is nicknamed, while the second-most significant bit fulfills the same role as in Generation III. This allows an unnicknamed Pokémon traded to a game of a different language to retain its name in the language of the previous game, but still change its name upon evolution.

The second-most significant bit specifies whether or not the Pokémon is an unhatched Egg or not.

The remaining 30 bits are the IVs, five bits apiece, in the order Sp. Def, Sp. Atk, Speed, Defense, Attack, and HP.

In other games

In Pokémon GO

In Pokémon GO, IVs have a range of 0 to 15. Pokémon have an IV for each of their three basic stats: HP, Attack, and Defense. In Pokémon GO, IVs are the only factor that can distinguish one Pokémon's stats from another's of the same species if they have the same Power Up level.